Galerkin–Vlasov Method for Deflection Analysis of Isotropic Sandwich Plates under Uniform Load | Journal of Engineering Sciences

Galerkin–Vlasov Method for Deflection Analysis of Isotropic Sandwich Plates under Uniform Load

Author(s): Mama B. O.1, Ike C. C.2*

1 University of Nigeria, Nsukka, 410101 Enugu State, Nigeria;
2 Enugu State University of Science and Technology, P.M.B. 01660, Enugu, Nigeria

*Corresponding Author’s Address:

Issue: Volume 5; Issue 1 (2018)

Paper received: January 27, 2018
The final version of the paper received: March 27, 2018
Paper accepted online: May 3, 2018

Mama B. O. Galerkin–Vlasov Method for Deflection Analysis of Isotropic Sandwich Plates under Uniform Load / B. O. Mama, C. C. Ike // Journal of Engineering Sciences. – Sumy : Sumy State University, 2018. – Volume 5, Issue 1. – P. D15-D19.

DOI: 10.21272/jes.2018.5(1).d3

Research Area: MECHANICAL ENGINEERING: Dynamics and Strength of Machines

Abstract. In this work, the Galerkin–Vlasov method was used to solve the governing partial differential equation of equilibrium for isotropic sandwich plates with simply supported edges (x = ±a, y = ±b) and under uniform load on the plate domain  Vlasov procedure was adopted in choosing the displacement shape functions as orthogonal eigen functions of dynamic Euler Bernoulli beams with equivalent spans, simple supports and loading as the plate. The resulting Galerkin-Vlasov equation was solved to obtain the unknown generalised shape function. It was found that the deflections obtained were exact solutions to the problem of bending isotropic sandwich plates. The deflection was found to be made up of two components: flexural deformation and shear deformation.

Keywords: isotropic sandwich plate; Galerkin–Vlasov method; governing differential equation of equilibrium; orthogonal eigen functions; generalized displacements parameters.


  1. Allen, H.G. (1969). Analysis and Design of Structural Sandwich Panels. Pergamon Press, Oxford.
  2. Balken, D., Azar, O., Turkmen, H. S., & Mecitoglu, Z. (2010). Transient response of a laminated sandwich plate with viscoelastic core subjected to air blast: Theory and experiment Structures under shock and impact. XI 113 WIT Transactions on The Built Environment, Vol. 113, doi.10.2495/sui00101.
  3. Magnucka, E., et al. (2013). Approximate solutions of equilibrium equations of sandwich circular plate. AIP Conference Proceedings, Vol. 1558, Issue 1(2352), doi: 10.1063/1.48260 13.
  4. Kinh, H. H. (1972). Analysis of Three Dimensional Orthotropic Sandwich Plate Structures by Finite Element Method. Ph.D. thesis, University Montreal.
  5. Kormaniková, E., & Mamuziċ, I. (2011). Shear Deformation Laminate theory used for sandwiches. Metabk, 50(3), pp. 193–196.
  6. Boen, L.-D. (1965). Theory of Bending of Multilayer Sandwich Plates. Ph.D. thesis, Oklahoma State University.
  7. Plantema, F. J. (1966). Sandwich Construction (The Bending and Buckling of Sandwich Beams, Plates and Shells). John Wiley & Sons, New York.
  8. Achilles, P. (1998). Design of sandwich structures. Ph.D. thesis, Cambridge University.
  9. Raville, M. E. (1955). Deflection and Stresses in a Uniformly loaded, Simply Supported Rectangular Sandwich Plate. FPL Report.
  10. Vinson, J. R. (2001). Sandwich Applied Mechanics Reviews, No. 54(3), pp. 201–214.
  11. Wang, C. M. (1995). Deflection of sandwich plates in terms of corresponding Kirchhoff plate solutions. Archive of Applied Mechanics, Vol. 65, Issue 6, 408–414.

Full Text

Scientific journal "The Journal of Engineering Sciences"
ISSN 2312-2498 (Print), ISSN 2414-9381 (Online).

Faculty of Technical Systems and Energy Efficient Technologies
Sumy State University